Matrices and Linear Algebra

by Schneider, Hans; Barker, George Phillip

• ISBN13: 9780486660141
• ISBN10: 0486660141
• Edition: 2nd
• Format: Paperback
• Copyright: 1989-06-01
• Publisher: Dover Publications

Summary

Basic textbook covers theory of matrices and its applications to systems of linear equations and related topics such as determinants, eigenvalues and differential equations. Numerous exercises, both true-false and multiple choice, with each chapter. Answer section.

Table of Contents

Preface to the Second Edition

Preface to the First Edition

The Algebra of Matrices

Matrices: Definitions

Addition and Scalar Multiplication of Matrices

Matrix Multiplication

Square Matrices, Inverses, and Zero Divisors

Transposes, Partitioning of Matrices, and Direct Sums

Linear Equations

Equivalent Systems of Equations

Row Operations on Matrices

Row Echelon Form

Homogeneous Systems of Equations

The Unrestricted Case: A Consistency Condition

The Unrestricted Case: A General Solution

Inverses of Nonsingular Matrices

Vector Spaces

Vectors and Vector Spaces

Subspaces and Linear Combinations

Linear Dependence and Linear Independence

Bases

Bases and Representations

Row Spaces of Matrices

Column Equivalence

Row-Column Equivalence

Equivalence Relations and Canonical Forms of Matrices

Determinants

Introduction as a Volume Function

Permutations and Permutation Matrices

Uniqueness and Existence of the Determinant Function

Practical Evaluation and Transposes of Determinants

Cofactors, Minors, and Adjoints

Determinants and Ranks

Linear Transformations

Definitions

Representation of Linear Transformations

Representations Under Change of Bases

Eigenvalues and Eigenvectors

Introduction

Relation Between Eigenvalues and Minors

Similarity

Algebraic and Geometric Multiplicites

Jordan Canonical Form

Functions of Matrices

Application: Markov Chains

Inner Produce Spaces

Inner Products

Representation of Inner Products

Orthogonal Bases

Unitary Equivalence and Hermitian Matrices

Congruence and Conjunctive Equivalence

Central Conics and Quadrics

The Natural Inverse

Normal Matrices

Applications to Differential Equations

Introduction

Homogeneous Differential Equations

Linear Differrential Equations: The Unrestricted Case

Linear Operators: The Global Vie?

Answers

Symbols

Index

Table of Contents provided by Publisher. All Rights Reserved.